....
however there little twist in Mercury program
the Suborbital flights were delay by Werner Von Braun, he wanted go save with another Redstone rocket test launch.
had He be overruled, Alan Shepard would have launch 16 day BEFOR Yurin Gagarin in Wostock 1
that had put the soviet serious behind in space race again..
On US space probe with success of Pioneer 0, it could also alter Who building the Probe launch and operate them: the USAF and not NASA
Actually the bit about Von Braun dragging out Mercury with the Redstones underscores my point--the American
leadership in the space program was in no hurry, from the President on down. They preferred to do it methodically and "right" and had confidence the American technology was ahead of Soviet. The panic always came from public perceptions of Western backwardness which were shamelessly manipulated for political purposes--including to be sure infighting among various factions who knew better.
Such as, say, the Air Force. The "bomber gap" and "Missile gap" panics were each cases of the Air Force, for reasons of its institutional prestige and funding, skewing the intelligence assessment task shamelessly. This is why the CIA was invented in the first place, to give dispassionate information to the President so his decisions would not be based on manipulated data.
So again, OTL it was Eisenhower who called for the formation of NASA and assigning it the mission of space science and Man In Space, and he did this for policy reasons having nothing to do with which team of rocket developers was the most competent. So the greater success of the Air Force ITTL (which again, apparently is a matter of them having plausible better luck in that particular launch, not of them being better than OTL) would not change anything. Army, Navy, and Air Force all had their rival ambitions; Ike wanted to short-circuit the whole question of which military outfit should "win" and assign whoever was good enough to civilian NASA to do the job of advancing American know-how (and prestige) in deep space. Unless the various services came up with strictly military reasons for putting soldiers or sailors in space, as they did come up with solid military reasons for launching unmanned spacecraft that were approved OTL; but he didn't want it perceived that the USA was trying to "conquer space" in the sense of "seizing the high ground" to threaten targets on Earth from or some such.
Meh, Pioneer 0 succeeding is a much bigger PR setback for the Soviets than Alan Shepard getting there first, because let's face it, a parabolic flight is much less impressive than an orbital one, while getting a probe out to the moon is way ahead of merely getting a probe into orbit.
Again that's my point; to technological insiders, the abilities the Soviets demonstrated with Sputnik were not news and in terms of developed and deployed capabilities the USA was still ahead, but in terms of general public perceptions it very pointedly demonstrated that the Russians were a people to be reckoned with. They in fact used essentially the same rocket to orbit Gagarin as they used to launch all the Sputniks. (And I believe that their OTL success in seeing the far side of the Moon first, which Michel has pointed out was by no means their first try, was also on an R-7 rocket, though I could be mistaken about that). Actually translunar orbits were already within the capabilities of the earliest rockets used by both sides; someone quite accidently, due to a launch failure late in the process, wound up sending one probe on the wrong trajectory--right out of the Earth-Moon system into an independent orbit around the Sun! By accident and as a mission failure.
The first US satellite, Explorer 1, was by all accounts superior to Sputnik 1. What mattered to the public was, it was second. Insiders knew full well it was second and not first because of policy reasons, not because it couldn't have been launched earlier for technical ones.
And those policy reasons had again to do with Corona, which was secret--Eisenhower wanted the first satellite, which he thought would be Vanguard, to be clearly civilian and scientific, because he feared the Soviets would try to make a fuss over a spy satellite orbiting over Russia--he felt a foot in the door in the form of a harmless satellite might help with a precedent. Then Khrushchev did him the favor of undercutting future Soviet objects much more surely than anything the US could do, by orbiting their satellite first with no by-your-leaves from any other nation.

After that the gloves were off and it was OK if the first satellite had obvious capabilities and was launched by an Army team involving a bunch of former Nazis. If Corona had been ready, and not bogged down in its long string of launch failures, one of them might have been the first US satellite--and not counted for a long time of course because it was secret.
So the point is, the POD makes little difference, except that the major Lunar far side features presumably don't get so many Russian names. The policy decisions about which agency gets what missions and at what pace each program should be pursued remain the same, on both sides of the Iron Curtain.
I could be wrong about what happens in Russia (which I guessed was, nothing much). But I'm pretty confident it would make little difference in the USA and if anything would tend rather to slow things down instead of speed them up.
Again it would be different if the reason Pioneer does not fail on launch is that the design and launch team was objectively better than OTL--but why and how would they be? The many failures of the early years were not because the teams were incompetent, it was because they were pioneering an unknown field and inevitable mistakes were how they learned their art, by expensive trial and error. Better luck on this one launch implies nothing about future launches, if anything tends to mask as yet undiscovered flaws and delay their rectification with a false glow of success.
That's why I think the Soviet leadership would have been tolerant of a few more slip-ups relative to OTL, particularly ones that involved the USA having a bit more luck. If they panicked at every disappointment and set-back they'd have abandoned space and rocketry decades ago; there had to be some tolerance in the Kremlin for the Soviet efforts to have been sustained at all.